Abstract
This paper deals with the development of a mathematical approach for the solution of linear, non-ageing viscoelastic materials undergoing mechanical deformation. The formulation is derived from integral approach based on a discrete spectrum representation for the creep tensor. Finite difference integration is used to discretize the integral operators. The resulting constitutive model contains an internal state variable which represents the influence of the whole past history of stress and strain. Thus the difficulty of retaining the strain history in computer solutions is avoided. A complete general formulation of linear viscoelastic stress-strain analysis is developed in terms of increments of stresses and strains. Numerical simulations are included in order to validate the incremental constitutive equations.
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Chazal, C., Moutou Pitti, R. Incremental constitutive formulation for time dependent materials: creep integral approach. Mech Time-Depend Mater 15, 239–253 (2011). https://doi.org/10.1007/s11043-011-9135-z
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DOI: https://doi.org/10.1007/s11043-011-9135-z